A major unsolved problem in computer science is the so-called P=NP problem: machines are considered in which there is a certain amount of freedom in choosing the next step in a computation (such machines are called non-deterministic). By making good guesses (or choices) one can often obtain a quicker computation than by systematically working through all possible cases in a deterministic way. The P == NP problem asks whether every function computable on a non-deterministic machine in polynomial (i.e., tractable) time is computable in polynomial time on ordinary (deterministic) machines.
-- N. J. Cutland, Computability. Cambridge University Press, 1980. p. 238.

Everything that can be invented has been invented. - Charles H. Duell, US Commissioner of Patents, in 1899.

Update: I've found several papers on the subject including Is the NP problem solved?. Haven't had a chance to read through them yet, but they look interesting.

The academic world? The Computing Science community? In the 80s and
the 90s, AI was defocussed on. It of course never disappeared, but it
certainly wasn't as prominent as in the late 70s and early 80s.

What were they referring to by AI?

Eh, "Artificial Intelligence"? ;-) Making complex decisions as fast
and in a similar way as humans can?

I just read through the paper you referred to, and it looks a bit
bullshit to me. P and NP problems are defined for Turing
machines, quantum machines are a fundamentally different class of
machines. There are other machines possible where it hardly makes
sense to talk about P and NP (take for instance an oracle and each
time your algorithm has to guess, you ask the oracle instead).

I do however have serious doubts about the feasability of quantum
computers. Perhaps when the NSA starts decrypting 4096 bit GPG
messages almost instantly I'll become a believer.

Generally I agree with this and your other post. AI has all the hallmarks of a degenerate research programme. But I did want to raise one point... ;-)

Eh, "Artificial Intelligence"? ;-) Making complex decisions as fast and in a similar way as humans can?

This combines what I would consider the two primary objectives of AI in a way that makes them sound like one.

AI as an investigative tool for a plausable model of cognition. Much work was invested into AI as a method to explain how we think we think. This research tended to be very domain specific and scaled poorly. It also had fundamental philosophical problems that put to lie many of the grandisoe claims that were made by it.

AI as an approach to solve problems that computers are typically bad at and humans are typically good at. This was a slighly more fruitful avenue. Usually the models bore little if any relationship to how we think we think. Examples of this are the AL work done in emergent phenomenon, GA's, neural networks.

The former appears to be almost totally abandonded. (Although high quality chess programs are perhaps one of its successes.) The latter is being used in a small number of unlikely areas with considerable success. (Chip design is a notable example)

Yves / DeMerphq
---
Writing a good benchmark isnt as easy as it might look.

I think there is a world market for maybe five computers. - Thomas Watson, chairman of IBM, 1943

There is no reason for any individual to have a computer in their home. - Ken Olsen, president, chairman and founder of Digital Equipment Corp., 1977

The telephone has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us. - Western Union internal memo, 1876

Airplanes are interesting toys but of no military value. - Marshal Ferdinand Foch, French commander of Allied forces during the closing months of World War I, 1918

The wireless music box has no imaginable commercial value. Who would pay for a message sent to nobody in particular? - David Sarnoff's associates, in response to his urgings for investment in radio in the 1920's

Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools. - New York Times editorial about Robert Goddard's revolutionary rocket work, 1921

It is possible to trisect any angle using only compass and straightedge.

The Internet has created a New Economy which is not bound by the rules of the old economy.

We happen to know (I hope) all of them are flat-out wrong. And each has been stated in the past as true. For some of them there is very little empirical evidence; for the rest, there is none.

The only question is: into which category are you putting AI? That people have been wrong is no argument, either way. So why repeat the point that people have incorrectly claimed that possible things are impossible? People have also correctly claimed that impossible things are impossible!